Second mortgage-How do i get one?

I already own one house which is in joint names with my ex partner, and i have been trying to get the deeds signed into my sole name but the mortgage lender has been stalling me, i started the process in April this year and still am no closer to the deeds being signed over. I am finding it a struggle to pay the mortgage that i have at the moment and am thinking about buying a cheaper house and sending back the keys to the old property, is this possible and how do i go about getting this process started. Is it possible to apply for another mortgage, when i already have one? If so, will high street mortgage lenders do this for me?